LES of steady spray flameand ignition sequences

in aeronautical combustorsS. Pascaud†∗, M. Boileau†, L. Martinez†, B. Cuenot† and T. Poinsot‡

†CERFACS, Toulouse, France ‡IMFT - CNRS, Toulouse, France

Ground ignition and altitude re-ignition are critical issues for aeronautical gas turbine design. They are strongly influ-enced by the turbulent flow structure as well as the liquid fuel spray and its atomization. Turbulent mixing, evaporation andcombustion that control the combustion process are complex unsteady phenomena coupling fluid mechanics, thermodynamicsand chemistry. To better understand unsteady combustion in industrial burners, Large Eddy Simulation (LES) is a uniqueand powerful tool. Its potential has been widely demonstrated in the context of turbulent cold flows, and it has been recentlyapplied to turbulent combustion. Its extension to two-phase turbulent combustion is a challenge but recent results confirm thatit brings totally new insight into the physics of flames for both mean and unsteady aspects. In the present work, an Euler-Eulerformulation of the two-phase flow equations is coupled with a sub-grid scale model and a turbulent combustion model. Theobtained two-fluid model computes the conservation equations in each phase and the exchanges source terms for mass andheat transfer between gas and liquid. Thanks to the compressible form of the gas equations, flame/acoustics interactions areresolved. For application to complex geometries, unstructured meshes are used. With this numerical tool, turbulent two-phaseflames are simulated in an industrial gas turbine. Some of the mechanisms involved in the steady spray flame are analysedand the partially premixed flame structure is detailed. Nevertheless, the capabilities of the LES technique for spray combus-tion are not limited to the stabilised spray flame. Unsteady complex phenomena such as ignition sequences give promisingresults : the unsteady behaviour of the reacting two-phase flow from the installation of a kernel to the possible propagationand stabilisation of the flame is computed and demonstrates the LES capabilities in such unsteady complex problems.

ContextThe main part of the production of energy comes from combustion of liquid hydrocarbon fuels, because of their con-venient way of storage and transport. Most of the current combustion chambers burn liquid fuel using injectors whichatomise, generally at high pressures, the liquid jet or film in small droplets (typically10 − 200 µm). Then, the fuelbecomes gaseous and an inhomogeneous mixing of air and vaporised fuel is created. For reasons of simplicity, thisfirst step of atomisation is supposed to be instantaneous and numerical tools for evaporation and gaseous combustionare applied to two-phase flow combustors. This allows to study the influence of the liquid phase on steady flames andignition sequences.The Large Eddy Simulations (LES) technique is used to understand unsteady phenomena occurring in turbulent spraycombustion. Many proofs of the LES capabilities are available for gaseous combustion1–6 but very few studies dealwith the complex topic of LES for two-phase reacting flows.7–10

The modelling of the liquid phase in a LES solver is an important issue for which two classes of methods are available :the Euler framework (EF) and the Lagrange framework (LF). The LF7 describes the liquid phase as a huge but finitenumber of droplets with their own trajectory, velocity, temperature and diameter while the EF,11,12 with an oppositepoint of view, considers the liquid phase as a continuous field whose characteristics are determined through a set ofconservation equations for the liquid volume fraction, the liquid phase velocity and temperature, and the first/secondorder moments of the size distribution. Several complex phenomena like droplet/droplet coalescence and collision ordroplet/wall interaction are easier to model in a LF. However, the choice of the EF is justified for a parallel computationof an unsteady spray combustion in a realistic combustor by the following arguments :Parallelism : LES in complex geometries needs high CPU time and requires parallel computing. However, the effi-cient implementation of LF on a parallel computer is a critical issue and implies good load balancing,13 whereas EF isdirectly parallelised with the same algorithms as the gas phase.Number of droplets : the LES technique is less dissipative than RANS methods. As a consequence, the number ofLagrangian droplets at each time step in each cell must be sufficient to provide a smooth and accurate continuous fieldof gaseous fuel. Because the fuel vapour distribution, directly produced by the discrete droplet evaporation sourceterms, controls the propagation of the front,14,15 this is crucial for two-phase flame computations. Very limited experi-ence on this question is available today but it is likely that combustion requires much more particles than usually donefor dispersion or evaporation studies, leading to uncontrolled CPU costs.

∗pascaud@cerfacs.fr

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Size distribution : since the spray granulometry controls the flame regime, a droplet size distribution must be consid-ered. LF is better on this question because it naturally discretises droplets with different sizes. However, recent studiesdemonstrate the EF capabilities to include polydispersed sprays.16–18

Inlet conditions : due to the atomisation complexity, the accurate determination of the spray characteristics is a criti-cal issue. Even if LF calculates droplet trajectories with precision, very approximate injection conditions will lead torough results. Close to the injector, the liquid spray is organised as dense blobs19 and LF can not be applied to thesehigh-loaded zones. As a contrary, EF is more compatible with the physics of liquid injection.

Numerical toolThe solverAVBP, developed atCERFACS, is a parallel fully compressible code which computes the turbulent react-ing two-phase flows, on both structured and unstructured grids, for complex industrial applications such as ignitionsequences or acoustic instabilities. Turbulent combustion modelling is ensured by the Dynamically Thickened Flamemodel,20 using a thickening factorF and an efficacity functionE to determine the flame front turbulent velocity.21

Subgrid scale turbulent viscosity is defined by the WALE model,22 derived from the classic Smagorinsky model.The Euler/Euler framework governing a turbulent reacting two-phase flow is composed, for each phase, of a set ofconservative equations defined by Eq. (1) and Eq. (2) and solved with the same numerical approach.

Carrier phase∂w∂t

+∇ · F = s (1)

Dispersed phase∂wl

∂t+∇ · Fl = sl (2)

For the carrier phase, the vector of conservative variables is defined by Eq. (3) withρ the density,(u1, u2, u3) thevelocity components,Et the total non chemical energy andYk the fuel mass fractions. The flux tensorF is composedof viscous, inviscid and subgrid scale components ands is the source term defined by Eq. (4). Combustion terms arethe reaction rateωk and the heat releaseωT modelled by an Arrhenius law.23 Additional source terms representingexchanges between phases are the mass transferΓ, the momentum transferIi and the enthalpy transferΠ.

w = ( ρu1, ρu2, ρu3, ρEt, ρYk) (3)

s = ( I1, I2, I3,E

FωT + Iiui + Π + ωspark,−E

Fωk + ΓδkF ) (4)

For the dispersed phase, the vector of conservative variableswl is defined by Eq. (5) withαl the volume fraction,(u1,l, u2,l, u3,l) the velocity components,hs,l the sensible enthalpy andnl the droplet number density. The flux tensorFl is only composed of convective terms and the source terms is defined by Eq. (6).

wl = (αlρl, αlρlu1,l, αlρlu2,l, αlρlu3,l, αlρlhs,l, nl) (5)

sl = (−Γ,−I1,−I2,−I3,−Π, 0) (6)

The fully explicit finite volume solverAVBPuses a cell-vertex discretisation and a second order time and space Lax-Wendroff centred numerical scheme.24 Characteristic boundary conditions NSCBC25 are used.

ConfigurationThe computed configuration is a 3D sector of 22.5-degrees of an annular aeronautical gas turbine at atmosphericpressure. The kerosene liquid sprayLS is located at the center of the main swirled inlet SI (Fig. 1). An annular seriesof small holes H are located around the inlet to lift the flame and protect the injector from high temperatures. Then,several holes on the upper and lower walls are divided in two parts. The first part of the combustor where combustiontakes place is located between the injector and the primary jets PJ, which bring cold air to the flame. The second partcalled dilution zone is located between PJ and dilution jets DJ, that reduce and homogenise the outlet temperature toprotect the turbine. The spark plug SP is located under the upper wall between two PJ (Fig. 2). The geometry (Fig. 3)also includes cooling films which protect upper and lower walls from the flame.The inlet and outlet boundary conditions are characteristic with relaxation coefficients to reduce reflexion.26 The SIimposed velocity field mimics the swirler influence. The other inlets are simple non-swirled jets. Non-slip conditionsare used on the upper and lower walls while symmetry condition is used on the chamber sides.15 µm-droplets areinjected at the SI center through a specific condition which specifies a liquid volumic fractionαl ' 10−3. The dropletsat288 K are heated by the air at525 K. The initial liquid velocity is equal to the gaseous velocity as the droplet Stokesnumber, based on the droplet relaxation time, is lower than one.

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The unstructured mesh is composed of 400000 nodes and 2300000 tetrahedra. The explicit time step is∆t ' 0.22µs.The mesh is refined close to the inlets and in the combustion zone (Fig. 4).The Arrhenius coefficients are fitted by a genetic algorithm27 from a reduced chemistry28 to the present one-stepchemistry :JP10 + 14 O2 ⇀↽ 10 CO2 + 8 H2O using criteria such as flame speed and thickness.

LSPJ DJSI

H

Fig. 1 Geometry sketch : side view

SP

Fig. 2 Geometry sketch : top view

Fig. 3 Complex geometry Fig. 4 Mesh refinement : central longitudinal view

Steady spray flamePrecessing Vortex Core

In its review on vortex breakdown, Lucca-Negro29 classifies the hydrodynamic instabilities appearing in swirled flows.For high swirl numbers, the axial vortex breaks down at the stagnation point S and a spiral is created around a centralrecirculation zone CRZ (Fig. 5) : this vortex breakdown is the so-called precessing vortex core (PVC) existing in alarge number of combustors.30 The LES technique capture the vortex breakdown in the combustor and its frequencyis evaluated with the backflow line on a transverse plane (Fig. 6) at six successive times marked with a number from1 to 6 and separated by0.5 ms. The turnover time is estimated atτswirl ' 3.5 ms, corresponding to a frequency offPV C ' 286 Hz. Moreover, the three rotating motions of the SI, the whole PVC structure and the spiral winding turnin the same sense, as illustrated by the rotating arrows on Fig. 5.

CRZ

PVC

S

SI

Fig. 5 Precessing Vortex Core Fig. 6 Backflow line : transverse cut plane

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Dispersion and evaporation

The15 µm droplets motion follows the carrier phase dynamics so that the CRZ of both zones are similar, as illustratedby both backflow lines on Fig. 7. Maintained by this CRZ, the droplets accumulate and the droplet number density,presented with the liquid volumic fraction field on Fig. 7, rises above its initial value. Increasing the residence time ofthese vaporising droplets, whose diameter field is presented on Fig. 8, makes the local equivalence ratio distributionreach values higher than10. The heat transfer linked to the phase change leads to the reduction of the gaseoustemperature, as shown by the isolineT = 450 K on Fig. 9, and an increase of the dispersed phase temperature. Thus,the CRZ, by trapping evaporating droplets, stabilise the vaporised fuel and the flame.

Fig. 7 Dispersion Fig. 8 Evaporation

Combustion

The flame front, illustrated on Fig. 9 by the heat release field, is influenced by both flow dynamics and evaporationrate. The main competitive phenomena for two-phase flame stabilisation are :

1. the air velocity must be low enough to match the turbulent flame velocity : the dynamics of the carrier phase(and in particular the CRZ) stabilise the flame front on a stable pocket of hot gases

2. zones where the local mixture fraction is within flammability limits must exist : combustion occurs between thefuel vapour radially dispersed by the swirl and the ambient air, where the equivalence ratio is low enough

3. the heat release must be high enough to maintain evaporation and reaction : the sum of heat fluxΠ and heatreleaseωT , plotted on Fig. 9, allows to identify the zone ( ) where the heat transfer due to evaporationextinguishes the flame :Π + ωT = 0.

In the present case, the flame front is stabilised by the CRZ (1.) but the heat release magnitude is reduced in theevaporation zone because of both effects (2.) and (3.). To determine the flame regime (premixed and/or diffusion),the Takeno indexT = ∇YF .∇YO and an indexed reaction rateω∗F = ωF

T|∇YF |.|∇YO| are used. The flame structure

is then divided into two parts :ω∗F = +ωF in the premixed regime part andω∗F = −ωF in the diffusion regime part(Fig. 10). In the primary zone, the partially premixed regime is preponderant because of the unsteady inhomogeneousfuel vapour. In the dilution zone, the unburned fuel reacts with dilution jets through a diffusion flame, as confirmed bythe coincidence between the flame and the stoichiometric line.

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Fig. 9 Flame front Fig. 10 Flame structure

PVC influence

The PVC, defined on Fig. 11a, controls the motions of both the vaporised fuel VF and the flame front. The cut plane,defined on Fig. 11a, is presented on Fig. 11b with the temperature field, the maximum fuel mass fraction (white lines)and the flame front (black isolines of reaction rateωF ). The CRZ stabilises hot gases and enhance evaporation leadingto a cold annular zone where the maximum fuel mass fraction precesses. The flame motion follows the PVC and thereaction rate is driven by the fuel vapour concentration.

a.

SI

b.

VF

Flame

b.

Fig. 11 PVC influence on evaporation and combustion

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Ignition sequenceSpark-like numerical method

The numerical method used to mimic an ignition by spark plug in the combustion chamber is the addition of the sourceterm ωspark in Eq. (4). This source term, defined by Eq. (7), is a gaussian function located at (x0, y0, z0) near theupper wall between both primary jets and deposited att = t0 = 0. The ignition delay, typical of industrial spark plugs,is σt = 0.16 ms.

ωspark =Espark

(2π)2σtσr3e− 1

2

[( t−t0

σt)2

+( x−x0σr

)2+( y−y0

σr)2

+( z−z0σr

)2](7)

Temporal evolution

The temporal evolution of the spark ignition is presented on Fig. 12 where the source termωspark, the maximum heatreleaseωT and the maximum temperature are plotted. First, the maximum temperature rises smoothly because of thesource term on energy equation. When this temperature is sufficient, the reaction occurs between fuel vapour and airleading to a sudden increase of the heat release of the exothermic reaction and then, the maximum temperature rapidlyrises. Once the source term is over, the maximum heat release decreases. The maximum temperature corresponds tothe hot gases : the ignition is successful.

15

10

5

0

ωspark

0.50.40.30.20.10.0 time [ms]

4500

4000

3500

3000

2500

2000

1500

1000

500

T [K]

6

4

2

0

ωT [kg.mm-3.s-1]

Source term ωspark Maximum heat release ωT

Maximum temperature

Fig. 12 Source termωspark, maximum heat releaseωT , maximum temperature

The sequence of ignition is illustrated on the longitudinal central cut plane on Fig. 13 with the fuel mass fractionfield and the reaction rate isolines, where the first image is presented att = 0.2 ms and after, successive images areseparated by∆t = 0.2 ms. At the beginning of the computation, the15 µm droplets evaporate in the ambient airat T = 525 K creating a turbulent cloud of vaporised fuel in the whole primary zone. This fuel vapour distribution,whose stabilisation is ensured by the CRZ, propagates from the evaporation zone to the spark plug area. Att = 0, thespark ignition occurs leatding to the creation of a hot kernel. The propagation of the flame front created by this pocketof hot gases is highly controlled by the fuel vapour distribution betweent = 0 andt = 1 ms. Once the flame frontreaches the CRZ (t ' 1 ms), there is no more vaporised fuel and the flame must evaporate the fuel droplets leadingto an increase of the maximum fuel mass fraction in the CRZ. This evaporation process stabilise the flame front asexplained in the previous section on steady spray flame.

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0.2 ms 0.4 ms 0.6 ms 0.8 ms

1.0 ms 1.2 ms 1.4 ms 1.6 ms

1.8 ms 2.0 ms 2.2 ms 2.4 ms

Fig. 13 Flame front propagation on fuel mass fraction field (white : 0→ black : 0.35)

ConclusionsA steady spray flame in a realistic aeronautical combustor has been computed using the parallel LES Euler/Eulersolver AVBP. The influence of the dispersed phase on the flame motion has been highlighted, in particular the role ofthe evaporation process. The unsteady approach brings totally new insight into the physics of such complex reactivetwo-phase flows. Furthermore, it allows the computation of an ignition sequence from the formation of the firstspherical flame front to the stabilisation of the turbulent spray flame. To conclude, the LES technique is a powerfultool to mimic ignition sequences and understand turbulent spray flame structure in realistic combustors.

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